When I started the game I selected one name and before I left the vault I changed it to another. Both names are common names with the common spelling, but when I met up with Codsworth he still called me by the original name. Is there somewhere I can look to confirm the change took and if so, will this be a problem going forward?

I believe "ShowNameMenu" in the debug console will bring the naming menu back up and you can see if it took the new name. It's possible that it's a bug and it only checks once right after you set the name the first time.

EDIT: If you're on PC. If you're on a console I'm not sure where you can look to see your characters name. Maybe under stats or something?

If you are on console you can turn on subtitles in the settings menu and your characters name will show up on screen when they speak.

ShowNameMenu doesn't actually work. For me at least. A lot of commands from previous games do not work.

Also - i've had the same issue. I've changed the name before exiting the vault but the change did not register. You can see your name when you are loading saves and in Pip-Boy.

It also appears that the main save file is listed as your original name. I was not too far in so I just started over.